Compute the velocity scale

INTERFACE:

    subroutine wscale(Bfsfc,u_taus,d,wm,ws)

DESCRIPTION:

This routine computes the turbulent velocity scale for momentum and tracer as a function of the turbulent friction velocity, $u_*$, the "limited" distance, $d_$lim, and the total buoyancy flux, $B_f$, according to

$$w_\phi = \dfrac{\kappa u_*}{\Phi_\phi (\zeta)} \quad .$$ (225)

In this equation, $\Phi_\phi$ is a non-dimensional function of the stability parameter $\zeta=d_$lim$/L$, using the Monin-Obukhov length,

$$L = \dfrac{u_*^3}{\kappa B_f} \quad .$$ (226)

In stable situations, $B_f \ge 0$, the length scale $d_$lim is just the distance from the surface or bottom, $d$. Then, the non-dimensional function is of the form

$$\Phi_\phi = 1 + \zeta \; , \quad$$ (227)

and identical for momentum, heat, and tracers.

In unstable situations, $B_f < 0$, the scale $d_$lim corresponds to the distance from surface or bottom only until it reaches the end of the surface (or bottom) layer at $d=\epsilon h$. Then it stays constant at this maximum value.

The different functional forms of $\Phi_\phi(\zeta)$ for unstable flows are discussed in Large et al. (1994).

USES:

    IMPLICIT NONE

INPUT PARAMETERS:

 
    buoyancy flux (m^2/s^3)
    REALTYPE, intent(in)                :: Bfsfc
 
    friction velocity (m/s)
    REALTYPE, intent(in)                :: u_taus
 
    (limited) distance (m)
    REALTYPE, intent(in)                :: d

OUTPUT PARAMETERS:

 
    velocity scale (m/s)
    for momentum and tracer
    REALTYPE, intent(out)               :: wm, ws

REVISION HISTORY:

    Original author(s): Lars Umlauf